Glines graduated from Yale in 1955 with a BA in drama. As a writer in children’s television, he worked for seven years on Captain Kangaroo and for four years on Sesame Street. His play In The Desert Of My Soul was anthologized in Best Short Plays Of 1976. His musical Gulp!, written with Stephen Greco and Robin Jones, had a lengthy off-off-Broadway run in 1977.

His plays written for, and originally produced by The Glines, the non-profit organization for gay arts which he co-founded in 1976 with Barry Laine and Jerry Tobin, include On Tina Tuna Walk, In Her Own Words (A Biography of Jane Chambers), Men Of Manhattan, Chicken Delight, Body And Soul Murder In Disguise, Key West, and Heavenly Days. His last play, Butterflies And Tigers, based on stories of the Chinese people during the Cultural Revolution, had an extended run in New York City in 1998.

Glines won a Tony Award and a Drama Desk Award in 1983 as producer of Torch Song Trilogy. In his acceptance speech for the Tony, he was the first person ever to acknowledge his same-sex lover on a major awards show. He won the Drama Desk Award and a Tony nomination in 1985 as producer of As Is, and won the Drama Desk Award in 1994 for Whoop-Dee-Doo!